Below we focus on the superradiant instability with ultra-light scalars. Such BH-condensate systems have been widely studied for constraining the scalar properties and for the possible observation of the GW emission. It has been shown that the BH evolves along the Regge trajectories on the mass-spin plot if the superradiant effect is strong [1]}, [2]}. Consequently, there are “holes" on the Regge plot in which BHs cannot reside. Combing with the observed BH merger events, favored and unfavored scalar mass ranges can be identified [3]}, [4]}, [5]}. On the other hand, with the continuous GW generated by the BH-condensate, works has been done to study the possibility of resolving these systems from the backgrounds [1]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}. A difficulty is to distinguish them from other monochromatic GW sources, such as neutron stars. In Refs. [9]}, [14]}, it is proposed that the GW from the BH-condensate systems has a positive frequency drift due to self-gravity, while the GW from neutron stars has a frequency drift in the opposite direction. The unresolved BH-condensate systems have also been carefully studied as stochastic backgrounds for GW detectors [11]}, [12]}.
